Variable speed rotary electric machine

ABSTRACT

A variable speed rotary electric machine comprises a stator composed of a stator core and first and second stator windings wound on the stator core, and a cage rotor mounted rotatably within the stator and composed of a rotor core and rotor conductor disposed in a squirrel-cage configuration. The first stator winding is connected to an AC power supply of a fixed frequency. The second stator winding is connected to a power supply of a variable frequency. The first and second stator windings are so wound as to form, respectively, numbers of poles differing from each other. The rotor conductors of the cage rotor are electromagnetically coupled with the magnetic flux generated by the first and second stator windings, respectively, and so disposed as to form a number of poles which is intermediate between the number of the poles formed by the first stator winding and the number of poles formed by said second stator winding.

The present invention generally relates to an improvement of a variablespeed rotary electric machine and more particularly, an improvement of avariable speed induction rotary machine such as a variable speedinduction motor, or generator, using variable frequency control.

In recent years, as progress is made in the technology of variablefrequency devices, the induction motors and induction generators ofrelatively high stoutness attract increasingly attention as the variablespeed rotary electric machines.

In particular, the induction generators are used in place of synchronousgenerators employed heretofore as hydraulic turbine generators. Sincethe induction generator can generate electric power at a constantfrequency independent of variations in the rotating speed thereof byexcitation of variable frequency, it is possible to operate thehydraulic turbine at the most efficient rotating speed depending on itsvariable load. By way of example, when variation in the flow rate ofwater or in the load occurs in a hydraulic power plant where thesynchronous generator is employed, the flow rate of water supplied tothe hydraulic turbine sometimes referred to as a water wheel is soadjusted by means of a governor and/or a water flow regulating valvethat the synchronous generator be constantly, driven at a predeterminednumber of rotations to thereby output the electric power at apredetermined constant frequency. However, operation of the hydraulicturbine at the constant speed through regulation of the flow rate ofwater supply thereto incurs undesirably degradation in the efficiency ofthe hydraulic turbine. In contrast, in case the variable speed inductiongenerator mentioned above is employed, a constant frequency can beassured independent of the rotating speed, which means that thehydraulic turbine can always be driven at its most efficient rotatingspeed. Furthermore, the use of the variable speed induction generatorrenders it unnecessary to employ the heretofore required governor ofexpensive and complicated structure, to a great advantage.

The prior art and the present invention will be explained in conjunctionwith the accompanying drawings, in which:

FIGS. 1 and 2 are schematic views showing hitherto known variable speedgenerator-motor systems, respectively;

FIG. 3 is a schematic view illustrating a general arrangement of abrushless variable-speed generator-motor system according to anembodiment of the present invention;

FIG. 4 shows a sectional view taken along the line IV--IV in FIG. 3;

FIGS. 5 to 7 are views for illustrating the principle of the invention,in which FIG. 5 shows a coordinate system for illustrating thetheoretical analysis, FIG. 6 is a schematic front view showingdisposition of rotor bars, and FIG. 7 is a developed view of the same;

FIGS. 8a to 8c are characteristic views for illustrating relationshipsbetween the number of rotor bars and a magnetomotive force component;

FIGS. 9a and 9b and FIGS. 10a and 10b are views for illustratingstructure and the principle of operation of the generator-motor systemaccording to the invention by comparing with the hitherto known system;and

FIG. 11 is a schematic view showing a variable speed generator-motorsystem according to another embodiment of the invention.

A power system in which the above-mentioned advantageous variable speedinduction rotary machine is employed has been proposed, for example, inJapanese Patent Application Laid-Open No. 45022/1977 in which awoundrotor induction generator is used as a generator whose secondarywinding (rotor winding) is excited by an AC exciting current suppliedfrom a variable-frequency AC source which is adjusted at a frequencycorresponding to the rotating speed of the hydraulic turbine. With sucharrangement, it is possible to generate an electric energy at a constantfrequency even when rotating speed of the hydraulic turbine changes.Describing in some detail this known wound-rotor induction generator andthe associated control system by referring to FIG. 1 which shows a basicsystem structure thereof, the wound-rotor induction generator 1 isdriven by a hydraulic turbine 2 to generate electric energy which issupplied to a system bus 3.

The wound-rotor induction generator itself is composed of a stator 4 ofan annular configuration, a rotor 5 rotatably mounted within the stator4, and a current collector including a slip ring 6 and brushes 7 andmounted at an end of the rotor for supplying it with an excitingcurrent.

The annular stator 4 includes a stator core 8 having winding slotsformed in the inner peripheral surface thereof and a primary winding 9wound on the stator core as received within the grooves. On the otherhand, the rotor 5 includes a rotatable shaft 10, a rotor core 11 mountedon the shaft 10 for rotation integrally with it and having winding slotsformed in the outer peripheral surface, and a secondary winding 12 woundon the rotor core as received within the slots thereof.

Arrangement is made such that the secondary winding 12 is supplied witha part of the output power derived from the primary winding 9 by way ofa transformer 13 and a frequency converter 14. In FIG. 1, numeral 15denotes a switch interposed between the generator and the system bus 3,and 16 denotes bearings for supporting the shaft of the rotor 5.

In the system of the arrangement described above in conjunction withFIG. 1, the output frequency of the primary winding is controlled to beheld at a predetermined constant value (commercial frequency) f₁ with agiven number of rotation N_(R) (rpm) of the hydraulic turbine in amanner as mentioned below. Since the frequency f₂ of the secondarywinding is equal to difference between the output frequency f₁ of theprimary winding and the rotational frequency of the rotor, the followingrelationship applies: ##EQU1## where P represents the number of poles inthe induction machine. Accordingly, the frequency is controlled bydetecting the rotational frequency N_(R) by means of an existingrotational number detector and exciting the secondary winding 12 with analternating current of the frequency f₂ determined from the aboveexpression (1). In this way, the output frequency can be maintained at aconstant value with any given rotational speed. However, the controlsystem according to the prior application suffers from shortcomingsdescribed below. One of them can be seen in the fact that the currentcollector composed of the slip ring 6 and the brushes 7 has to beindispensably provided which requires troublesome maintenance from timeto time and undergoes abrasion to shorten the use life. Another drawbackis seen in that end portions of the rotor winding are subjected toenormously large stress under a centrifugal force and an electromagneticforce produced upon accidental failure (e.g. occurrence of shortcircuit), giving rise to a problem with regard to the mechanicalstrength. In a certain case, there may arise in reality damage andeventual destruction of the winding, leading to occurrence of a seriousaccident.

There is known a rotary machine of the type under consideration which isrelatively less susceptible to the drawbacks mentioned above. Forexample, reference may be made to Japanese Patent Publication No.21959/1982. More particularly, referring to FIG. 2 of the accompanyingdrawings, this known system includes a pair of induction machines 17 and18 which are mechanically coupled together by means of a coupling 19,wherein a secondary winding (rotor winding) 41 of the first inductionmachine 17 is electrically connected to a secondary winding 42 of thesecond induction machine through a connector 20. Since the primarywinding (stator winding) of the first induction machine 17 is directlyconnected to an AC bus 3, it is referred to as the main machine whilethe second induction machine 18 having a primary winding 44 is termed anexciter.

Operation of this system is as follows. Assuming that the primaryfrequency of the main machine 17 is represented by f_(M1) with thesecondary frequency thereof being represented by f_(M2), while theprimary frequency of the exciter 18 is represented by f_(E1) with thesecondary frequency thereof being represented by f_(E2), and that slipsin the main machine and the exciter are represented by S_(M) and S_(E),respectively, the following relations apply: ##EQU2## where N_(R) is thenumber of revolutions of the hydraulic turbine, P_(M) is the number ofpoles in the main machine and P_(E) is the number of poles in theexciter.

As will be apparent, the primary frequency f_(M1) (i.e. frequency of theAC current obtained from the primary winding) of the main machine can bemaintained at a predetermined constant value (e.g. commercial frequency)by supplying a current of the frequency f_(E1) which is determined onthe basis of the detected revolution number N_(R) in accordance with theexpression (4) to the primary winding of the exciter through a frequencyconverter 14, even when the number of revolutions of the hydraulicturbine undergoes any variation. With this arrangement, the so-calledbrushless structure in which the provision of the current collector isunnecessary can be realized, whereby the problem of the troublesomemaintenance can be solved, bringing about an advantage in this respect.However, this arrangement is accompanied with a disadvantage in that twoinduction machines are required, involving increased size and cost ofthe system. As an attempt to deal with this problem, it is conceivableto mount two sets of rotor windings on a single rotor in a duplexwinding structure with an iron core being used in common so that a pairof induction machines may be considered to be implemented in a singleintegral unit. However, the structure of the rotor windings will thenbecome much complicated, involving a problem in the manufacture inpractice. Furthermore, great difficulty will be encountered insupporting the end portions of the rotor windings, resulting in that theadequate mechanical rigidness or strength can not be assured.

For reinforcing the mechanical strength, it might be considered toreplace the rotor of the wound-rotor structure by a cage orsquirrel-cage rotor. As is well known, the cage rotor is characteristicof a much simplified and rigid structure of the winding end portion inwhich an end ring is simply bonded to the rotor conductors or bars.

However, in case the conventional cage rotor is combined with the statorof the structure described hereinbefore, i.e. the stator provided withthe duplicated or double windings which are supplied with currents ofmutually different frequencies, respectively, it is impossible tocontrol one of the stator winding currents by the other depending on therevolving speed, unlike the case of the aforementioned wound-rotorinduction generator, because excitation is effected at either one of thefrequencies even if the current of a variable frequency is supplied toone of the windings. Thus, the combination can operate as a usualgenerator, but not as a variable-speed generator with a constant outputfrequency.

In view of the foregoing, it is an object of the present invention toprovide a variable speed rotary electric machine which is substantiallyimmune to the drawbacks of the hitherto known machines described aboveand in which one of the stator winding currents can be controlled by theother in accordance with the revolving speed even when the rotor isrealized in a squirrel-cage structure.

According to the present invention, there is provided a variable speedrotary electric machine which includes a stator composed of a statorcore provided with first and second stator windings and a squirrel-cagerotor, wherein the first stator winding is connected to an AC powersupply source of a constant frequency while the second stator winding isconnected to an AC power supply source of a variable frequency. Thefirst and second stator windings are so wound as to form differentnumbers of poles, respectively. On the other hand, the squirrel-cagerotor is provided with conductor bars whose number is adapted to form anintermediate number of poles between the number of poles formed by thefirst stator winding and that of the second stator winding.

In the following, the invention will be described in detail inconnection with an exemplary embodiment thereof by referring to FIGS. 3and 4. FIG. 3 is a schematic view showing a variable speed rotaryelectric machine, more particularly a variable speed generator-motorsystem according to an embodiment of the invention. In FIG. 3, the sameparts as those shown in FIG. 1 are denoted by like reference numerals.Referring to FIG. 3, the rotary induction machine shown as enclosed by asingle-dotted line block 21 includes a stator 40 having a stator core 8wound with duplicate or double windings for generating two revolvingmagnetic fields which differ from each other in the number of poles, anda cage rotor provided with rotor bars whose number is selected to have aspecific relation to the numbers of poles of the respective statorwindings according to the invention. In FIG. 3, reference numerals 22and 23 denote, respectively, first and second primary windings of thestator. In the following description, the winding 22 will be referred toas a main winding while the winding 23 will be termed an excitingwinding. A reference numeral 24 denotes the rotor bars, and 25 denotesend rings serving for electrically connecting the rotor bars at bothends of the rotor, respectively. It should be noted that in the case ofthis embodiment, the rotor bars 24 are provided in a number which liesbetween the numbers of poles formed by the stator windings 22 and 23,respectively. In the case of the embodiment of the invention shown inFIG. 4, it is assumed that the primary winding forms eight poles, theexciting winding has four poles and that the number of the rotor bars isselected equal to six. A reference numeral 26 denotes an air gap betweenthe stator and the rotor, 27 denotes slots formed in the stator core, 28denotes a rotatable shaft and 29 denotes a spider.

Next, the principle of operation of the variable speed generator-motorsystem according to the illustrated embodiment of the invention will bedescribed.

In the first place, the reason for which the system can operate as avariable speed system when the above mentioned relationship isestablished between the numbers of stator poles and the number of therotor bars will be elucidated. FIG. 5 shows a coordinate system used forthe theoretical analysis to be discussed hereinafter, in which thecoordinate associated with or fixed on the stator is represented byθ_(s) while the coordinate associated with or fixed on the rotor isrepresented by θ_(R) which is displaced in phase by ##EQU3## from thecoordinate θ_(s). These coordinates are shown in the state developed inthe circumferential direction, wherein θ_(s) thus indicates a value ofspatial displacement from a predetermined origin on the stator. On theother hand, θ_(R), indicates a spatial displacement of the rotor in therotation thereof from the original set at a point on the rotor surfacewhich corresponds to θ_(s) of zero (i.e. the original of thestator-associated coordinate system). Further, ω_(M1) represents anangular frequency of the main winding current of the stator, ω_(E1)represents an angular frequency of the exciting winding current of thestator, and ω₂ represents an angular frequency of the current of therotor conductors (bars). Disposition of the end ring and the rotor barsis schematically illustrated in FIGS. 6 and 7, wherein the rotor bararray shown in FIG. 6 is illustrated in FIG. 7 in the state developed inthe circumferential direction. Referring to these figures, when thenumber of the bars is represented by N with a bar pitch beingrepresented by α_(b) , the following relation applies:

    N.α.sub.b =2π                                     (5)

In the stator-associated coordinate system, the voltage V_(M) of themain winding and the voltage V_(E) of the exciting winding for u-, v-and w-phases, respectively, can be given by the following expressions(6) and (7), respectively. ##EQU4##

Both the expressions (6) and (7) represent the three-phase balancedvoltages. It is noted that the exciting winding is connected in thenegative phase sequence relative to the primary winding. Further, theprimary winding current i_(M) and the exciting winding current i_(E) (ofthe stator) for u-, v- and w-phases, respectively, are given by thefollowing expressions (8) and (9), respectively. ##EQU5##

Both expressions 8 and 9 represent the three-phase balanced currents. Bythe way, description about the exciting current for generating theexciting magnetic flux is not important for elucidation of the operationunder consideration and thus omitted.

Next, a magnetomotive force generated under the applied voltages isdetermined. More specifically, a composite magnetomotive force of thestator and the rotor is expressed as follows: ##EQU6## where p_(M) :number of pole pairs in the main winding,

P_(E) : number of pole pairs in the exciter, and

m: m-th harmonic wave.

In the above expression (10), the first term represents themagnetomotive force of the stator produced by the main winding and thesecond term represents the magnetomotive force of the stator produced bythe exciting winding. The third to fifth terms represent themagnetomotive force of the rotor bars, wherein the third term representsa unipolar component, i.e. a magnetomotive force of axial direction, thefourth term represents a positive-phase-sequence component, and thefifth term represents a negative-phase-sequence component. Themagnetomotive force of the rotor bars contains harmonic components whosevalues vary in dependence on the number of the bars. Amplitudes of thecomponents represented by the third to fifth terms are given by theexpressions (11) to (13), respectively. The expression (14) gives a barcurrent at the n-th bar. The current flowing through the bars containscomponents relating to the number of poles of the main winding and thenumber of poles in the exciting winding and other harmonic components invarious combinations.

By the way, to meet the requirement for continuity of the currentthrough the rotor bars, the following condition must be satisfied:##EQU7## Accordingly, the unipolar component given by the expression(11) and hence the third term of the expression (10) are zero.

In view of the expression (16), the expressions (12) and (13) may berewritten in the orderly forms as follows: ##EQU8##

By replacing the expressions (5) and (14) in the expressions (17) and(18), the latter can be rewritten in the orderly forms as follows:##EQU9##

Next, examination will be made on the magnitude of the harmoniccomponents which are induced in the main winding constituting one of thestator windings when a voltage is applied to the exciting windingconstituting the other of the stator windings in compliance with theexpressions (19) and (20) during rotation of the cage rotor of simplexwinding. It is known that when the winding factor of the stator is 1.0and the rotor is a so-called solid rotor in which the whole surface iscovered by conductors, only the magnetomotive force corresponding to therevolving magnetic field produced by the stator is generated. However,in view of the fact that the solid rotor is subjected to a significanteddy current loss, it is common in practice to use the cage rotorprovided with conductor bars disposed in the slots. Since the number ofthe conductor bars of the cage rotor is limited, the gap magnetomotiveforce includes a large number of harmonic components. FIGS. 8a to 8cillustrate the relationships between the number of the rotor bars andharmonic components produced by the stator winding and contained in thegap magnetomotive force on the assumption that the stator is of a duplexwinding type and that the rotor is of a simplex cage winding type. Therelation illustrated in FIG. 8a corresponds to the case where the polenumber P_(M) of the main winding is equal to eight and the pole numberP_(E) of the exciting winding is four. The relation illustrated in FIG.8b corresponds to the case where the pole number P_(M) is 12 and P_(E)is 8. The relation illustrated in FIG. 8c is based on the conditionsthat P_(M) =18 and that P_(E) =12. It will be seen from the figures thatthe harmonic component generated by the main winding of poles in numberP_(M) is of such magnitude which can be controlled from the side of thestator, for example, by controlling the frequency, voltage and/or phaseof the excitation, provided that the number of the rotor bars liesbetween the pole numbers P_(M) and P_(E) of the stator. In thisconnection, it goes without saying that the magnetomotive forcecorresponding to the pole number P_(E) of the exciting winding isgenerated regardless of the number of the rotor bars since the voltageis applied to the exciting winding. It will further be seen that in casethe number of the rotor bars is not in the range between the polenumbers P_(M) and P_(E), e.g. when the number of rotor bars is 22, 36 or44 as is usually the case of the cage rotor, the magnetomotive componentP_(M) due to the main winding of the stator is scarcely generated.

In order to assure the operation similar to that of the hitherto knownbrushless wound-rotor induction machine shown in FIG. 2, themagnetomotive components corresponding to the pole number P_(M) of themain winding and the pole number P_(E) of the exciting winding mustnecessarily be produced in the gap. This requirement can be fullysatisfied when the number of the rotor bars lies between the polenumbers P_(E) and P_(M).

Next, the principle of operation of the brushless squirrel-cageinduction machine according to the invention will be elucidated incomparison with the hitherto known brushless wound-rotor type inductionmachine by referring to FIGS. 9a and 9b and FIGS. 10a and 10b. As willbe seen in FIGS. 9a and 9b, the primary circuit (stator circuit) is ofidentical configuration in both the woundrotor induction machine (FIG.9a) and the squirrel-cage induction machine (FIG. 9b). Concerning thesecondary circuit (rotor circuit), the three-phase balanced windings areconnected in the negative phase sequence in the case of the wound-rotorinduction machine (FIG. 9a). The current flowing through the primaryexciting winding generates the revolving magnetic field having the polenumber P_(E). When the secondary winding 42 of the pole number P_(E) isintersected by the revolving magnetic field, a current flow is inducedin the secondary winding 42. Since the secondary winding 42 of the polenumber P_(E) is electrically connected to the secondary winding 41 ofthe pole number P_(M), the current flows naturally to the secondarywinding 41 as well. Consequently, the rotor produces two magnetic fieldsof the pole numbers P_(E) and P_(M) , respectively, in the course ofrotation thereof, even though the current flowing through the windingsis of a single frequency. The revolving magnetic field of the polenumber P_(M) generated by the rotor intersects the primary main winding43 of the pole number P_(M) to induce a current of the frequencycorresponding to the pole number P_(M) in the primary main winding. Inthis way, the machine operates as the generator.

On the other hand, in the case of the squirrelcage induction machineshown in FIG. 9b, the rotor is of a simplex end-ring structure in whichthe bars are connected through a single end-ring and has rotor barswhose number is intermediate between the pole number P_(E) of theexciting winding and the pole number P_(M) of the main winding. As willbe seen from FIGS. 8a to 8c, since the gap magnetomotive force containsthe components corresponding to the pole numbers P_(E) and P_(M) andhaving fully controllable magnitude, there takes place a phenomenonsimilar to the case in which the rotor of the wound-rotor type forms twomagnetic fields of the pole numbers P_(E) and P_(M), respectively in thecourse of rotation. However, since the squirrel-cage rotor is providedwith a reduced number of the conductor bars which are considerablyspaced from each other, a number of other harmonic components aregenerated. In this respect, the squirrel-cage machine differs from thewound-rotor type machine.

FIGS. 10a and 10b show equivalent circuits of the induction machineshown in FIGS. 9a and 9b, respectively. Referring to FIGS. 10a and 10b,the induction machine is equivalent to the circuit which includes a pairof transformers having respective secondary windings connected to eachother, wherein values of voltage (or current) and frequency of theprimary main winding can be varied in correspondence to variation in thevoltage applied to the primary exciting winding as well as frequency ofthe current flowing therethrough.

Referring to FIG. 10b and assuming that the current flowing through theprimary main winding 22 has a frequency f_(M1), the current flowingthrough the exciting winding 23 is of a frequency f_(E1), the currentflowing through the rotor bars is of a frequency f₂ and that the numberof rotation is N_(R), following relations apply valid: ##EQU10## whereP_(M) : number of poles in the main winding, and

P_(E) : number of poles in the exciting winding.

As will be seen from the expression (22), the frequency f_(M1) of thecurrent flowing through the main winding can be constantly maintained ata predetermined value by correspondingly controlling the frequencyf_(E1) of the current flowing through the exciting winding on the basisof the detected rotation number.

From the foregoing description, it will be appreciated that there hasbeen provided according to an embodiment of the invention a variablespeed rotary electric machine which can be implemented in a simplifiedbrushless cage structure of increased rigidness and in which thefrequency of the current flowing through one of the stator windings canbe controlled by correspondingly controlling the frequency of thecurrent flowing through the other stator winding in dependence on therevolving speed, whereby the drawbacks of the hitherto known machinesdescribed hereinbefore can be satisfactorily eliminated.

Although the description has been made on the assumption that theinvention is applied to a variable speed generator system equipped witha prime mover such as a hydraulic turbine, it goes without saying thatthe invention may be equally applied to a variable speed motor systemfor driving a pump, fan or the like.

FIG. 11 shows another embodiment of the present invention which differsfrom the preceding one in that double end rings are provided at each ofboth ends of the rotor. In the figure, numerals 30 and 31 denote the endrings, respectively, and 32 denoted an insulation for insulating the endrings 30 and 31 from each other. With this structure, improvement of thewaveform can be accomplished by dividing each of the rotor bars intoseveral strips while assuring the same function as that of the systemshown in FIG. 3 without giving rise to a problem such as leakage betweenthe adjacent bar strips because of insulation interposed between theadjacent end rings, whereby the aimed object can be attained in arelatively facilitated manner, to another advantage.

In the foregoing description, it has been assumed that the first statorwinding is supplied with a current of commercial frequency. However, itis obvious that an AC current of other frequency or DC current may bealternatively supplied to the first stator winding.

There has now been provided according to the invention a variable speedrotary electric machine which comprises a stator composed of a statorcore wound with first and second stator windings and a rotor ofsquirrelcage type, wherein the first stator winding is connected to anAC power supply of a predetermined fixed frequency while the secondstator winding is connected to a power supply of variable frequency, andwherein the first and second stator windings are so wound as to formmagnetic poles in different numbers, respectively, while the cage rotoris provided with a number of bars which form an intermediate number ofmagnetic poles between the numbers of poles formed by the first andsecond stator windings, respectively. With this structure, themagnetomotive force prevailing in the gap contains the magnetomotivecomponents of controllable magnitude in correspondence to the magneticpoles formed by the first and second stator windings. By virtue of thisfeature, the cage rotor can be realized in a brushless structure, whilethe frequency of the current flowing through one of the stator windingscan be controlled by correspondingly varying the frequency of thecurrent flowing through the other stator winding in dependence on therevolving speed.

We claim:
 1. A variable speed rotary electric machine, comprising astator having first and second stator windings wound on a stator coreand a cage rotor mounted rotatably within said stator and including arotor core and rotor conductors constituting a cage rotor winding,wherein said first stator winding is connected to an AC power supply ofa constant frequency while said second stator winding is connected to apower supply of variable frequency, said first and second statorwindings being so wound as to form magnetic poles in numbers differingfrom each other, the rotor conductors of said cage rotor beingelectromagnetically coupled with magnetic fluxes generated by said firstand second stator windings and so disposed as to form magnetic poleswhose number is intermediate between the number of magnetic poles formedby said first stator winding and the number of magnetic poles formed bysaid second stator winding.
 2. A variable speed rotary electric machineaccording to claim 1, wherein the number of the rotor conductors of saidcage rotor is so selected as to correspond to an average of the numbersof poles formed by said first and second stator windings.
 3. A variablespeed rotary electric machine according to claim 1, wherein the rotorbars of said cage rotor are realized in a multiple cage structure, therotor conductors constituting respective cages being electricallyindependent of one another.
 4. A variable speed rotary electric machine,comprising a stator having first and second stator windings wound on astator core and a cage rotor mounted rotatably within said stator andincluding a rotor core and rotor conductors constituting a cage rotorwinding, wherein said first stator winding is connected to an AC powersupply of a constant frequency and said second stator winding isconnected to a power supply of variable frequency, said first and secondstator windings being adapted for simultaneous energization by saidconstant frequency power supply and said variable frequency powersupply, respectively, said first and second stator windings being sowound as to form magnetic poles in numbers differing from each other,the rotor conductors of said cage rotor being electromagneticallycoupled with magnetic fluxes generated by said first and second statorwindings and so disposed as to form magnetic poles whose number isintermediate between the number of magnetic poles formed by said firststator winding and the number of magnetic poles formed by said secondstator winding.
 5. A variable speed rotary electric machine according toclaim 4, wherein the number of the rotor conductors of said cage rotoris so selected as to correspond to an average of the number of polesformed by said first and second stator windings.
 6. A variable speedrotary electric machine according to claim 4, wherein the rotor bars ofsaid cage rotor are realized in a multiple cage structure, the rotorconductors constituting respective cages being electrically independentof one another.
 7. A variable speed rotary electric machine according toclaim 4, wherein said stator having said first and second statorwindings wound on said stator core is a non-rotatable member.